Answer :
positive sloping linear graph with hole at negative 3, negative 1 intersecting the x axis at negative two and the y axis at two
Answer:
The graph of given function is shown below.
Step-by-step explanation:
The given function is
[tex]f(x)=\frac{x^2+5x+6}{x+3}[/tex]
Factorize the numerator.
[tex]f(x)=\frac{x^2+3x+2x+6}{x+3}[/tex]
[tex]f(x)=\frac{x(x+3)+2(x+3)}{x+3}[/tex]
[tex]f(x)=\frac{(x+2)(x+3)}{x+3}[/tex]
Cancel out the common factor.
[tex]f(x)=x+2[/tex]
It is a straight line because it is a one degree polynomial.
At x=0,
[tex]f(0)=0+2=2[/tex]
The y-intercept of the function is (0,2).
Put f(x)=0
[tex]0=x+2[/tex]
[tex]x=-2[/tex]
The x-intercept of the function is (-2,0).
Equate the cancel factor equal to 0, to find the hole of the function.
[tex]x+3=0\Rightarrow x=-3[/tex]
The function has hole at x=-3.
The graph of given function is shown below.
